%0 Journal Article
%T Positive solutions for some Riemann-Liouville fractional boundary value problems
%A Bachar, Imed
%A MÃ¢agli, Habib
%J Journal of Nonlinear Sciences and Applications
%D 2016
%V 9
%N 7
%@ ISSN 2008-1901
%F Bachar2016
%X We study the existence and global asymptotic behavior of positive continuous solutions to the following
nonlinear fractional boundary value problem
\[
(p_\lambda)
\begin{cases}
D^\alpha u(t)=\lambda f(t,u(t)),\,\,\,\,\, t\in (0,1),\\
\lim_{t\rightarrow 0^+}t^{2-\alpha} u(t)=\mu, \quad u(1)=\nu,
\end{cases}
\]
where \(1 < \alpha\leq 2; D^\alpha\) is the Riemann-Liouville fractional derivative, and \(\lambda,\mu\) and \(\nu\) are nonnegative constants
such that \(\mu + \nu > 0\).
Our purpose is to give two existence results for the above problem, where \(f(t; s)\) is a nonnegative
continuous function on \((0; 1)\times[0;\infty)\); nondecreasing with respect to the second variable and satisfying some
appropriate integrability condition. Some examples are given to illustrate our existence results.
%9 journal article
%R 10.22436/jnsa.009.07.12
%U http://dx.doi.org/10.22436/jnsa.009.07.12
%P 5093--5106